Question regarding Ph.D. at UK universities v. USA

Hello all. I am currently a student at the LSE in an MSc program for
Global Politics. I desire to earn a PhD and use that in academia back
in the USA. I was thinking of applying either to the LSE or
Oxford/Cambridge for their PhD program. It is a 3 year program,
requires no classes, nor teaching experience. It is straight
dissertation research.

I would like to know if I am employable at the collegiate level back
in the states; namely, at a 4 year university. Is it a respectable
degree? As in, will hiring faculty back at 4 year institutions scoff
at this degree in relation to the differences with their programs?
Please advise!

Thanks